Equations of Motion of a Vehicle in a Moving Fluid

Dife culties with the differing sets of equations used for submersibles, airships, and airplanes are removed by treating the effects of the inertial and added masses as separate functions of the inertial and relative velocities. The equations of motion of a rigid vehicle moving in a perfect e uid are then derived for the case where the e uid mass is accelerating and contains velocity gradients. The classic perfect e uid moments and forces for straight, curved, and convergent e ows arerecovered. It is shown that the differing sets of equations normally used for submersibles, airships, and aircraft can also be recovered as special cases, but in an augmented form that includes the effects of e uid motion and velocity gradients. In addition, it is shown how the resultant perfect e uid equations may be augmented to include viscous forces and moments derived from other theoretical or experimental sources.